Seasonal Autoregressive Integrated Moving Average Modelling and Forecasting of Monthly Rainfall in Selected African Stations

Abstract

Africa as a continent is blessed with arable land suitable for crop production but this cannot be fully harnessed without proper understanding of the rainfall pattern.Modelling and forecasting rainfall in Africa is even more important now considering the climate change that has brought a new narrative into the rainfall pattern globally, Africa inclusive.This study applied Seasonal Integrated Moving Average (SARIMA) models in modelling and forecasting rainfall across five selected African stations with one station each from the five African regions: West (Abuja, Nigeria), East (Nairobi, Kenya), South (Pretoria, South-Africa), North (Cairo, Egypt) and Central Africa (Yaoundé , Cameroon).Monthly rainfall data for these stations between 1980 and 2022 (42 years) were obtained from the MERRA-2 satellite.However, the data for this study were obtained from the solar radiation data archive website (www.soda-pro.com).The Soda service provides time series of solar radiation data derived from satellites.Furthermore, Modern-Era Retrospective Analysis for Research and Application-2 (MERRA-2) data were extracted from the satellite, which included meteorological and atmospheric data.Since January 1980, the data has been available in hourly, daily, and monthly increments.However, missing data values were checked and removed before implementing the analysis in this study.The determination of the specific SARIMA parameters orders for each city was carried by manual tuning after observing the plots of the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF).Descriptive analysis revealed that Abuja had the highest variance in the amount of rainfall compared with other major cities in Africa while rainfall in Yaoundé between March and June was higher than that of other stations.Monthly rainfall was stationary in all the stations as shown by the result of Augmented Dickey (p<.05) except for Yaoundé which was stationary after the first differencing.Based on the result of outof-sample forecast performance, different SARIMA models were found to be suitable for rainfall in each of the stations with ARIMA (0,0,1) (1,0,1)12 for Abuja (RMSE=70.7044)and Nairobi (RMSE=92.8925),ARIMA (1,0,1) (1,0,1)12 for Cairo (RMSE=9.9279),ARIMA (2,0,0) (1,0,1)12 for Pretoria (RMSE=42.05462)and ARIMA (1,1,1) (1,0,1)12 for Yaoundé (RMSE=79.42084).The findings show that the seasonal terms were statistically significant in all models which justified the use of seasonal ARIMA models in modelling rainfall in these selected stations in Africa.This also underscored the significant role of the season in the rainfall pattern in the selected African stations.Findings also revealed that the previous month's rainfall has a positive influence on the present month's rainfall in some of the stations.